A262076 The first of seven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of thirteen consecutive positive integers.

26, 598, 90688, 1891916, 285495236, 5955760408, 898738921678, 18748731881906, 2829229839956546, 59021002008489118, 8906414637444294568, 185798095573991870996, 28037390449444799352956, 584892345845924401415728, 88261696228437590918820358

Offset

1,1

Comments

For the first of the corresponding thirteen consecutive positive integers, see A262077.

Links

Colin Barker, Table of n, a(n) for n = 1..572

Index entries for linear recurrences with constant coefficients, signature (1,3148,-3148,-1,1).

Formula

a(n) = a(n-1)+3148*a(n-2)-3148*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: -26*x*(x^4+22*x^3+317*x^2+22*x+1) / ((x-1)*(x^4-3148*x^2+1)).

Example

26 is in the sequence because 26^2 + ... + 32^2 = 5915 = 15^2 + ... + 27^2.

Mathematica

LinearRecurrence[{1, 3148, -3148, -1, 1}, {26, 598, 90688, 1891916, 285495236}, 20] (* Vincenzo Librandi, Sep 11 2015 *)

Prog

(PARI) Vec(-26*x*(x^4+22*x^3+317*x^2+22*x+1)/((x-1)*(x^4-3148*x^2+1)) + O(x^20))
(Magma) I:=[26, 598, 90688, 1891916, 285495236]; [n le 5 select I[n] else Self(n-1)+3148*Self(n-2)-3148*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Cf. A262074, A262075, A262077.

Sequence in context: A293612 A197123 A203598 * A057010 A217636 A249863

Adjacent sequences: A262073 A262074 A262075 * A262077 A262078 A262079

Keyword

nonn,easy

Author

Colin Barker, Sep 10 2015

Status

approved